Answer:
(3,-5)
Step-by-step explanation:
Given
[tex]M = (2,2)[/tex]
[tex]H = (1,9)[/tex]
Required
Determine G
This is calculated using the following midpoint formula;
[tex]M(x,y) = (\frac{x_1 + x_2}{2},\frac{y_1 + y_2}{2})[/tex]
Where
[tex](x,y) = (2,2)[/tex] and [tex](x_1,y_1) = (1,9)[/tex]
Substitute these values in the formula above
[tex](2,2) = (\frac{1 + x_2}{2},\frac{9 + y_2}{2})[/tex]
Solving for [tex]x_2[/tex]
[tex]2 =\frac{1 + x_2}{2}[/tex]
Multiply both sides by 2
[tex]2 * 2 = 1 + x_2[/tex]
[tex]4 = 1 + x_2[/tex]
[tex]x_2 = 4 - 1[/tex]
[tex]x_2 = 3[/tex]
Solving for [tex]y_2[/tex]
[tex]2 = \frac{9 + y_2}{2}[/tex]
Multiply both sides by 2
[tex]2 * 2 = 9 + y_2[/tex]
[tex]4 = 9 + y_2[/tex]
[tex]y_2 = 4 - 9[/tex]
[tex]y_2= -5[/tex]
Hence, the coordinates of G is [tex](3,-5)[/tex]
